When trades from separately managed accounts are pooled for execution, the realized market-impact cost can be far greater than the sum of the predicted cost over all accounts. Multi-portfolio optimization is a technique for rebalancing multiple portfolios at the same time, considering their joint effects while adhering to account-specific constraints. The interaction of accounts in a multi-portfolio setting can bias particular accounts if fairness is not considered in the solution methodology.
With respect to the trading of multiple accounts, fairness is not well-defined. Definitions vary among portfolio managers often based on their particular investment offering. For this reason, we do not prescribe a single best approach for multi-portfolio optimization. Instead, we discuss the pros and cons of two approaches that each has foundations in economic theory, the Cournot-Nash equilibrium and the collusive solution. We present a unified framework capable of solving either problem.